Finite Group Databasebeta

← #11778580

Subgroups — #11778580

Order 1152.

630 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#544C211yesmaximal, characteristic
2#10592742C212yesmaximal
3#10592680C211yesmaximal, characteristic
4#10589404C212yesmaximal
5#10589394C211yesmaximal, characteristic
6#71898—34nomaximal
7C32×C4⋊Q8—22no—
8C32×#125—22no—
9C32×C22⋊Q8—21no—
10C32×C22⋊Q8C2212yes—
11C32×#117—21no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15#63662—22no—
16#63658—21no—
17#63658C2211yescharacteristic
18#63657C2212yes—
19#63635—22no—
20C3×#544D314yes—
21#5043—38no—
22#4981—34no—
23#4538—38no—
24#4528—34no—
25C2×C32×Q8—21no—
26C2×C32×Q8D412yes—
27C22×C32×C4D411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3—21no—
32C32×C4⋊C4—21no—
33C32×C4⋊C4—21no—
34C32×C4⋊C4—21no—
35C32×C4⋊C4—22no—
36C32×C4⋊C4—22no—
37C32×C4⋊C4—22no—
38C32×C4⋊C4D412yes—
39C32×C22⋊C4—22no—
40C32×C42—22no—
41C4⋊(C3⋊Dic3)—22no—
42#3750—42no—
43C2×C3⋊(C3⋊C8)—22no—
44#1611—91noSylow
45C3×C4⋊Q8—28no—
46C3×#125—28no—
47C3×C22⋊Q8—24no—
48C3×C22⋊Q8C2×D318yes—
49C3×#117—24no—
50C2×C3×C4⋊C4C2×D314yes—
51C2×C4⋊Dic3—34no—
52C2×Dic3⋊C4—64no—
53#835—68no—
54C3⋊#95—34no—
55C3⋊#95—64no—
56#830—38no—
57#808—68no—
58C23×C32C2×D411yescharacteristic
59C32×Q8—42no—
60C32×Q8—81no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—22no—
64C2×C32×C4—22no—
65C2×C32×C4—21no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4SD1612yes—
69C2×C32×C4C2×D412yes—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3—41no—
76C3⋊(C3⋊C8)—42no—
77#544C3⋊D311yescharacteristic
78#483—92no—
79#398—91no—
80#328—92no—
81#324—91no—
82C2×C3×Q8—24no—
83C2×C3×Q8#6718yes—
84C22×C3×C4#6714yes—
85C22×C3×C4#6714yes—
86C22×C3×C4C22×D314yes—
87C22×Dic3—64no—
88C22×Dic3—64no—
89C3×C4⋊C4—24no—
90C3×C4⋊C4—24no—
91C3×C4⋊C4—24no—
92C3×C4⋊C4—28no—
93C3×C4⋊C4—28no—
94C3×C4⋊C4—28no—
95C3×C4⋊C4#6718yes—
96C3×C22⋊C4—28no—
97C3×C42—28no—
98C4⋊Dic3—68no—
99Dic3⋊C4—128no—
100C2×C3⋊C8—68no—
101C22×C32—21no—
102C22×C32—21no—
103C22×C32#12011yescharacteristic
104C22×C32C2×SD1611yescharacteristic
105C22×C32#13711yescharacteristic
106C32×C4—22no—
107C32×C4—22no—
108C32×C4—42no—
109C32×C4—41no—
110C32×C4—42no—
111C3⋊Dic3—42no—
112C3⋊Dic3—81no—
113C4⋊Q8—22no—
114#125—22no—
115C22⋊Q8—21no—
116C22⋊Q8C2×C3⋊D312yes—
117#117—21no—
118C2×C4⋊C4—91no—
119C2×C4⋊C4—181no—
120C2×C4⋊C4C2×C3⋊D311yescharacteristic
121#106—182no—
122#103—182no—
123C22⋊C8—92no—
124#95—91no—
125#95—181no—
126C23×C3C2×#6714yes—
127C3×Q8—48no—
128C3×Q8—84no—
129C2×C3×C4—24no—
130C2×C3×C4—24no—
131C2×C3×C4—28no—
132C2×C3×C4—28no—
133C2×C3×C4—24no—
134C2×C3×C4—44no—
135C2×C3×C4—44no—
136C2×C3×C4#21518yes—
137C2×C3×C4C2×#6718yes—
138C2×Dic3—68no—
139C2×Dic3—124no—
140C2×Dic3—124no—
141C2×Dic3—124no—
142C2×Dic3—124no—
143C2×Dic3—124no—
144C3⋊C8—128no—
145C2×C32—21no—
146C2×C32—21no—
147C2×C32#44811yescharacteristic
148C2×C32#45611yescharacteristic
149C2×C32#45811yescharacteristic
150C2×Q8—21no—
151C2×Q8#63812yes—
152C22×C4—181no—
153C22×C4—181no—
154C22×C4#63811yescharacteristic
155C22×C4#63811yescharacteristic
156C22×C4C22×C3⋊D311yescharacteristic
157C2×C8—182no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—182no—
165C4⋊C4—362no—
166C4⋊C4#63812yes—
167C22⋊C4—22no—
168C42—22no—
169C22×C3—24no—
170C22×C3—24no—
171C22×C3C2×#21514yes—
172C22×C3#94214yes—
173C22×C3#95314yes—
174C3×C4—28no—
175C3×C4—28no—
176C3×C4—44no—
177C3×C4—48no—
178C3×C4—48no—
179Dic3—128no—
180Dic3—244no—
181C32#161111yescharacteristic, complemented, Sylow
182C23C2×#63811yescharacteristic
183Q8—42no—
184Q8—81no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—182no—
193C2×C4—361no—
194C2×C4—361no—
195C2×C4—361no—
196C2×C4—361no—
197C2×C4—361no—
198C2×C4#375512yes—
199C2×C4C2×#63812yes—
200C8—362no—
201C2×C3—24no—
202C2×C3—24no—
203C2×C3#522714yes—
204C2×C3#524314yes—
205C2×C3#524614yes—
206C22—21no—
207C22—21no—
208C22C2×#375511yescharacteristic
209C22#6415111yescharacteristic
210C22#6416211yescharacteristic
211C4—22no—
212C4—22no—
213C4—41no—
214C4—42no—
215C4—42no—
216C4—362no—
217C4—721no—
218C3#7189814yescomplemented
219C2—21no—
220C2—21no—
221C2#1059292611yescharacteristic
222C2#1059294211yescharacteristic
223C2#1059294511yescharacteristic
subgroupG/H
centerC22#64162
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#544C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenter#544C3⋊D3
hypocenterC32#1611
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
181. C32#1611semidirect
218. C3#71898semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×#5442
#105927422
#105926802
#105894042
#105893942
#718983